UNIT CONVERSION  Inches of Water to PSF


 Gwendoline Brooks
 2 years ago
 Views:
Transcription
1 PROPERTIES OF AIR/VELOCITY UNIT CONVERSION  Inches of Water to PSF PURPOSE: To Illustrate to the student the procedure for converting Inches Of Water to PSF and canceling units. 1) Often times in the study of aeronautics conversion tables or conversion factors are used to convert a reading taken from the instrumentation into another unit. This is required to keep all units the same in the equation 2) For example a reading in Inches of water must be converted to pounds per square foot (PSF). (pounds abbreviated = lbs) 3) This is accomplished by multiplying the inches of water by ( 14.7 PSI / Inches of water). To convert lbs per square inch to lbs per square foot multiply inches by 144 (number of square inches in one square foot) 4) Due to the fact units are being used in all the equations the process for canceling the units becomes very important.
2 PROPERTIES OF AIR/VELOCITY EXAMPLE: The units inches of water will cancel leaving the result in PSI (pounds per square inch) RESULT: 14.7 / = X 25 = PSI IS THE CONVERSION FACTOR TO CONVERT INCHES OF WATER TO POUNDS PER SQUARE INCH
3 LESSON PLAN VENTURI INSERT Recommend as prerequisites: Lesson Plan: Lesson Plan: Lesson Plan Unit Conversion Properties of Air Air Velocity Measurement Lesson Plan: Venturi Insert is divided into 3 progressive levels: Level I Students are provided the area rule formula. Students practice solving the formula for area and velocity. Using venturi insert A students calculate areas and predict velocities. Students compare their predictions to actual velocities measured in the wind tunnel. A lab report is written reporting the findings. Level II Students are provided the Bernuolli formula. Using venturi insert A students calculate areas, predict pressures, and velocities. Students compare their predictions to actual pressure and velocities measured in the wind tunnel. A lab report is written reporting the findings. Level III Students are introduced to the concept of flow separation and backflow. Students are provided a venturi design criteria chart. Venturi B geometry is provided to the students for them to measure. (Venturi B is poorly designed by intent) Students are asked to predict the performance of Venturi B. Students compare their predictions to actual pressure and velocities measured in the wind tunnel. A lab report is written reporting the findings.
4 LESSON PLAN I VENTURI INSERT Level I Title: Law of Continuity Introduction: The continuity equation can be used to explain why the flow of a fluid (or air) will change velocity due to the shape of an object. Lesson: 1) In aeronautics the shape of an airfoil will create lift. This is accomplished by increasing the velocity of air over the airfoil. 2) This velocity change because of the shape is due to the Law of Continuity. This law states Density x Area x Velocity = Constant 3) At velocities less than the speed of sound (subsonic) density will not vary. Density can be deleted and the formula can be simplified to AREA x VELOCITY = CONSTANT 4) As fluid flows through a tube and the area (cross section) of the tube changes the velocity of the fluid will change in relation to the area. 5) At low speeds air will have the same properties as a fluid therefore water or fluids can be used to demonstrate these principles. Examples: 1) Water flowing in a river. Ask your students what they think will happen to the speed (velocity) of water flowing in a river as the river banks get narrower. (Area of the river is decreased) 2) Water flowing over a rock 3) Air flowing threw an hour glass shaped object (Venturi) 4) Ask students to think of other examples of objects that effect the speed of air or water
5 TITLE: Continuity Math Worksheet LESSON PLAN I VENTURI INSERT Level I Introduction: The following problems are designed to use with the wind tunnel to verify the answers. The data was collected using a venturi in the test section. Problems: Use the formula V 1 x A 1 = V 2 x A 2 to solve for the following: Change the formula to: V1 = 50 mph A1 = 23.4 A 2 = 29.4 V 2 = V 1 x A 1 A 2
6 LESSON PLAN I VENTURI INSERT Level I Area Rule Practice: All answers should be in standard units. (1) Compute the Velocity (V2) at location 2 for the following problems: (a) A1 = 5 ft 2 V1 = 50 ft / sec A2 = 10 ft 2 (b) A1 = 20 ft 2 V1 = 5 ft / sec A2 = 10 ft 2 (c) A1 = 2 ft 2 V1 = 4 miles / hr A2 = 1 ft 2
7 LESSON PLAN I VENTURI INSERT Level I (2) A 12 inch diameter pipe carries water at a velocity of 15 ft / sec. The pipe must be reduced to 4 inch diameter to fit through a wall. What will the velocity of the water be in the section that fits trough the wall? 4 inch diameter pipe through wall 12 inch diameter pipe 3) Brainstorming Activity: Have students think of other places where they have seen the shape of an object change the speed of air or water. Write there applications below:
8 Laboratory Experiment: Title: Venturi Insert Activities Objective: To obtain a reading from the wind tunnel test section venturi A and use this readings to calculate the velocity at a second point. Safety: Before Operating the Wind Tunnel perform operational run sheet instructions. Tools and equipment: Venturi (A) test section Inserts, 2 Dwyer water manometers, 10 tube water manometer and tygon tubing. Procedure: 1) Remove second countersunk screws and nuts from the front of the test section ( both sides top and bottom) 2) Connect correct tygon numbered tubes to the lower venturi (numbers go at the opposite end from venturi). 3) Install the upper venturi A section centered in the top of the test section using long wood screws (place washer under screws). 4) Feed the 10 tygon tubes from the lower section through the hole in the center of the test section. As the venturi is brought into place continue pulling tubes (be careful not to disconnect tubes). 5) Once the venturi is centered in the lower test section Install the short wood screws to secure venturi. 6) To aid the airflow tape the leading edge of the venturi sections to the tunnel floor. 7) Connect the numbered tubes to the 10 tube water manometer. 8) Run the wind tunnel and confirm the level of the water in the tubes agrees with the shape of the venturi. If not check for leaks. 9) Using tee fitting connect Dwyer water manometer to the #3 and #8 static ports. 10) Run the wind tunnel and adjust velocity reading from #3 to 45 MPH.
9 11) Measure the distance from the two venturi sections at #3 and #8 static ports. Lines are on the upper test section opposite of the lower ports. 12) Calculate the Area at #3 and #8 ports: Remember Area = Length x Width Test section width = 6.0 if the distance at #3 = 3.9 Area = 6.0 X ) Complete Continuity Math formula to solve for velocity at #8 probe. 14) Run the wind tunnel and check agreement of your answer. (Your answer should agree within 5% of calculated reading.) 15) Repeat the experiment using different velocities. 16) Complete the Continuity Table Area calculation table: Static port # Tunnel Width Distance Between Ports AREA
10 LESSON PLAN VENTURI INSERT Level I Prepare a run sheet that converts the desired set point velocity in miles/hr to feet/second to be read on probe #1. Also include columns for theoretical values of the velocity reading at probe #2 in feet per second and in miles per hour. Compare these to the actual velocities measured by running this experiment under the supervision of your instructor. Write in the actual velocity readings in your run log. Write a lab report discussing your procedure and results. EXPERIMENT #1 Proof of Area Rule Date of Experiment: Purpose: Team Members:
11 LESSON PLAN VENTURI INSERT Level II Teacher s Notes Title: Air Velocity Measurement Calculation Introduction: Velocity ( speed of the air ) is obtained from reading the air pressure. Lesson: 1) To perform aeronautical calculations we must be able to measure the velocity of the air. One of the more accurate means to accomplish this is to use Bernoulli s equation: As the velocity increases  pressure decreases 2) By using a pressure reading in Inches of Water (pressure) we are able to calculate the velocity of the air. 3) Several steps must be taken to modify Bernoulli s equation for the purpose we need. P T = P S 1 + ρ v 2 2 VELOCITY must be moved to the left side of the equation P T P ρ v 2 S = To solve for P Subtract the Wind Tunnel Total pressure From the static pressure reading 1 2 P = 1 2 ρ v 2 2 P = ρ v 2 To simplify ROH ρ Multiply P x 2
12 To move ROH to the left side of the equation 2 ρ P = v 2 To solve for velocity squared take the square root of the left side 2 ρ P = v We are now able to solve for velocity by taking the square root of P x 2 divided by Given the following static pressure readings solve for velocity remember the pressure readings are in inches of water and must first be converted to PSF (Inches of water x x 144) NOTE: For our purposes tunnel pressure is considered to be 0 To convert feet per second to miles per hour (mph) multiply by SAMPLE PROBLEM: 1) Convert (4.07) in. H20 to Velocity Step 1) P = (4.07)  0 = 4.07 in. H20 Step 2) 4.07 x = PSI x 144 = PSF Step 3) 2 x P = Step 4) / = 17, Step 5) sq root of 17, = feet per second(fps) Step 6) x.6818 = mph Answer: 91 mph
13 BERNOULLI FORMULA PRACTICE All answers should be in standard units. VENTURI INSERT Level II (1) Compute the pressure related to a velocity of: (a) 100 ft/sec 2 (b) 100 miles/hr (2) What velocity exists if the following pressure is measured? (a) 75 lb/ft 2 (b) 0.25 lb/in 2 (c) 5 in H 2 0 (3) At the entrance to a tunnel test section the area is 2 ft 2. The pressure is measured to be 1 in H 2 0. Compute the pressure at the exit of the test section where the area is 2 ft 2.
14 Laboratory Experiment Level II Title: Air Velocity Calculation Objective: The student will be able to calculate the air velocity in the wind tunnel using the Bernoulli formula. Set up a spreadsheet to enter the data and formula for velocity Safety: Before operating the wind tunnel perform operational run sheet Tools and Equipment: Venturi A test section insert, 2 Dwyer water manometers, 10 tube water manometer and tygon tubing Procedure: 1) Remove second countersunk screws and nuts from the front of the test section ( both sides top and bottom) 2) Connect correct tygon numbered tubes to the lower venturi (numbers go at the opposite end from venturi). 3) Install the upper venturi A section centered in the top of the test section using long wood screws (place washer under screws). 4) Feed the 10 tygon tubes from the lower section through the hole in the center of the test section. As the venturi is brought into place continue pulling tubes (be careful not to disconnect tubes). 5) Once the venturi is centered in the lower test section Install the short wood screws to secure venturi. 6) To aid the airflow tape the leading edge of the venturi sections to the tunnel floor. 7) Connect the numbered tubes to the 10 tube water manometer. 8) Run the wind tunnel and confirm the level of the water in the tubes agrees with the shape of the venturi. If not check for leaks. 9) Using tee fitting connect Dwyer water manometer to the #3 and #8 static ports. 10) Run the wind tunnel and adjust velocity reading from #3 to 1 Water 11) Calculate the velocity in MPH and FPS solve for velocity at probe #8 and determine the correct reading in Inches of Water. 12) Repeat this experiment at several tunnel velocities (at least 3). Create a
15 spreadsheet in column format that computes the predicted pressures and velocities from the area you measured. The second section of the spreadsheet should calculate the velocity from the measured pressure. Make a column that computes the difference between the measured and predicted velocity. This is the absolute error. In the final column, divide the absolute error by the predicted velocity. This is called the relative error. Your relative error should be less than +/ 5%. 13) Write a lab report discussing your procedure and results. You should discuss the accuracy of your results. In particular, discuss the difference between predicted, calculated, and measured values. Which is the correct result? Date of Experiment: Purpose: Team Members: DESIRED TUNNEL VELOCITY: ACTUAL TUNNEL VELOCITY: TAP # AREA PREDICTED VELOCITY PREDICTED PRESSURE MEASURED PRESSURE CALCULATED VELOCITY Observations:
16 LESSON PLAN I VENTURI INSERT Level III Teacher s Notes: The 3rd level incorporates advanced critical thinking and analysis. Students will be given engineering diagram charts to interpret. These charts are not based on exact formulas. A second venturi insert is provided which violates the design charts. Students should be able to use the charts to predict the poor performance. They should be recognize the scientific principle that explains the difference between data obtained and the calculated data. A venturi has a design limitation based on the geometric angle of divergence. The area of the tunnel or venturi decreases from the entrance to the throat of the venturi. The throat of the venturi is the minimum area. After that point, the flow area will increase. As an exercise in Level III you will have the students plot the pressure using knowledge from Levels I & II (area rule and Bernoulli s equation) versus distance in the venturi from entrance to exit. They should note that will from the entrance to the throat the pressure decrease as the area decreases. Then after the throat the area increases so the pressure will decrease. Ask the students if they think there will be any difference in the flow quality before and after the throat. (There will be.) Air flow naturally wants to move from high pressure to low pressure (give an example of letting air out of a balloon). The students should see that the pressure in the venturi does move from high pressure to low pressure in the entrance. But after the throat the flow is going from low to high pressure. This is unnatural and will only occur when air is forced. Students should recognize that it is possible something different should happen. Refer to figure 1. In the inlet, since the air is being compressed (low to high pressure) it can easily follow converging (or decreasing area) wall angles. It can do so up to 45. Show the venturi or venturi drawing to the students to illustrate this. However, since the flow does not move from the low pressure to high pressure as well, it can not follow the wall diverging (increasing area) angle. If this angle is too great, the flow will separate. (this provides an insight to stall in the next lesson plan) This means that there is an area near the wall where the velocity is near zero. In extreme cases, flow in the opposite direction may occur (backflow). In practice what this means is the equations are no longer accurate if you exceed a divergence angle of 10. Venturi B does have a divergence angle of greater than 10 and the data will not agree with predictions. The error increases with velocity and area. This concept of a difference between assumptions and measurements is referred to in the Proficiency Test. The Venturi Design Chart provides the design criteria.
17
18 PRESSURE PROFILE WORKSHEET LESSON PLAN I VENTURI INSERT Level III Using the chart provided compute the pressure through the venturi form the inlet through the throat and from the throat to the exit. The locations of the pressure taps are provided. The pressure at these locations should be plotted plus a point halfway in between each tap. Do this for each venturi on the graph provided. Discuss with the class and your teacher your results. Is there a difference in the pressure before and after the venturi throat? The chart provided is a venturi design chart. If a venturi is well designed it should perform well. Good performance is defined if the actual pressure and velocity readings agree with the calculated values. If a venturi is poorly designed the measured values will not agree with the calculated. The chart requires that you measure the certain dimensions on the venturi. Do this on the worksheet provided. VENTURI Length, L Width, W Angle, Θ 2 x Θ Stall? A B According to the venturi design chart which venturi is a better design?
19 LESSON PLAN I AIRFOIL SECTION Level I AIRFOIL TERMINOLOGY The following terms will be used in this lesson plan: Leading Edge  The front of the airfoil (tip). Trailing Edge  The aft (rear) edge of the airfoil. Chord or Chordline  An imaginary straight line which passes through an airfoil or wing section from the leading to trailing edge. Chord Length  Distance between the leading and trailing edges of an airfoil. Angle of Attack  The angle formed between the wind striking an airfoil and the chordline of the airfoil. Camberline (meanline)  a line connecting all points midway between the upper and lower surfaces of the airfoil. Camber  A perpendicular distance between the shoreline and the camberline. Symmetrical Airfoil  A airfoil that has the same shape on both sides of its centerline. Asymmetrical Airfoil  A airfoil that has a different upper shape than lower shape. (cambered airfoil). Wing Span  The length of an aircraft wing (when the aircraft is viewed headon). Delta  Difference between static and dynamic pressure ( Ρ). Roh ρ  air density at standard day ( slugs per cubic foot). Alpha α  angle of attack in degrees. Coefficient  A dimensionless number used to express magnitude.
20 LESSON PLAN I AIRFOIL SECTION Level I AIRFOIL GEOMETRY
21 LESSON PLAN I AIRFOIL SECTION Level I SCALING LAW Geometric Similarity is the engineering term used to describe the rules that allow a scale model of an aerodynamic object to be tested. Usually, due to limited space, an object is scaled down. An example is a 1/32nd scale hobbymodel aircraft. Engineers use scale models to test various designs and learn about basic theory. Each dimension of the object should be scaled in order to be geometrically similar. In the above example, the length, height, and width would be multiplied by 1/32. An F16 aircraft that has a wing span of 31 ft., a length of 47 ft., 8 in., and a height of 16 ft. 5 in. The wing area is square feet. At this scale, the model would have a wing span of 11 5 / 8 in., a length of 1 ft., 5 7 / 8 in., and a height of 6 1 / 8 in. The wing area would be 4 5 / 8 square inches. Note that since area has two dimensions, the full scale number was divided by (1/32) squared. In order to isolate the primary force, sometimes only one dimension is scaled. An example is the difference between scaling a wing (area) and an airfoil (length). Since the airfoil shape is usually constant at any point along the span of the wing, the airflow characteristics or pressure over the wing section will be the same all along the wing span. The primary force due to the pressure doesn t change along the wing span. However, as will be seen in the experiments, the pressure changes dramatically along the chord. This is why the wing is scaled in only one direction  the chord. This deliberate scaling in only one direction is called the characteristic dimension. There are some differences due end effects. End effects are from the fuselage and the wing tip can also be tested. This generally has small effects on lift. The airfoil characteristic dimension is the chord length, c (see figure). The ratio between the chord length of the tunnel model airfoil and the prototype airfoil is the scale of the model. The chord lengths must be in the same units so that the scale will be dimensionless. When the geometric similarity occurs, the primary forces on the object will also be scaled. For the airfoil example, the primary force is lift. Therefore if a 1/10th scale airfoil is tested in a wind tunnel, the lift measured will be 1/10th of the lift on the fullscale airfoil. To obtain the lift expected on the fullscale airfoil, multiply by 10. In order to minimize the effect of scaling on the answer, and also to eliminate confusion over whether English or SI units are chosen, aerodynamic forces are expressed in dimensionless coefficient form. The actual physical parameter (force or pressure) is divided by a combination of geometric and flow conditions. The specific combination of parameters has generally been identified in advance from historical research.
22 If the nondimensionalizing parameter has been properly chosen, it will cause data taken at many different conditions to collapse to a single line, thus eliminating the need to take data at each and every condition. (Incidentally, identification of nondimensional parameters by a researcher is a worthy achievement. It usually signifies an new understanding of a phenomenon and leads to engineering development). The first dimensionless coefficients used in this lesson plan is the pressure coefficient. The pressure coefficient (sometimes called the coefficient of pressure) is defined as: C p = P s P ( ρ / g o ) V Where the following symbols are defined as: C p = Pressure Coefficient (dimensionless). P s = Pressure in physical units on airfoil surface ( lb / ft 2 ). P = Pressure in physical units at infinity ( lb / ft 2 ). r = Density ( lb / ft 3 ). g 0 = Gravitational constant (32.2 ft / sec 2 ). V 0 = Tunnel Velocity ( ft / sec ). As you can see the units cancel: [( lb / ft 2 )( ft / sec 2 )]/[( lb / ft 3 )( ft / sec ) 2 ]. The quantity in the denominator is called the dynamic pressure, q. It has units of pressure and is the pressure caused by velocity. C p = P s P q This formula can be manipulated when taking data in the wind tunnel, using the following physical interpretation (since the reading is often referenced to the atmospheric pressure): P s = P reading + P atm and P = P tunnel static P s  P = P reading + P atm  P tunnel static If there are no losses in the tunnel, the total pressure is equal to the atmospheric pressure. P s  P = P reading + P total  P tunnel static
23 The dynamic pressure was defined earlier as the difference between the total and static pressures. (See the general and Venturi lesson plans). P total = P tunnel static + P dynamic P total = P tunnel static + q rearranging; P total  P tunnel static = q P s  P = P reading + ( P total  P tunnel static ) = P reading + q So finally, the wind tunnel format for pressure coefficient is: C p = P + rdg q q P rdg = q + 1
24 PROPERTIES OF AIR/VELOCITY UNIT CONVERSION  Inches of Water to PSF PURPOSE: To Illustrate to the student the procedure for converting Inches Of Water to PSF and canceling units. 2) Often times in the study of aeronautics conversion tables or conversion factors are used to convert a reading taken from the instrumentation into another unit. This is required to keep all units the same in the equation 3) For example a reading in Inches of water must be converted to pounds per square foot (PSF). (pounds abbreviated = lbs) 4) This is accomplished by multiplying the inches of water by ( 14.7 PSI / Inches of water). To convert lbs per square inch to lbs per square foot multiply inches by 144 (number of square inches in one square foot) 5) Due to the fact units are being used in all the equations the process for canceling the units becomes very important.
25 PROPERTIES OF AIR/VELOCITY EXAMPLE: The units inches of water will cancel leaving the result in PSI (pounds per square inch) RESULT: 14.7 / = X 25 = PSI IS THE CONVERSION FACTOR TO CONVERT INCHES OF WATER TO POUNDS PER SQUARE INCH
26 LESSON PLAN VENTURI INSERT Recommend as prerequisites: Lesson Plan: Lesson Plan: Lesson Plan Unit Conversion Properties of Air Air Velocity Measurement Lesson Plan: Venturi Insert is divided into 3 progressive levels: Level I Students are provided the area rule formula. Students practice solving the formula for area and velocity. Using venturi insert A students calculate areas and predict velocities. Students compare their predictions to actual velocities measured in the wind tunnel. A lab report is written reporting the findings. Level II Students are provided the Bernuolli formula. Using venturi insert A students calculate areas, predict pressures, and velocities. Students compare their predictions to actual pressure and velocities measured in the wind tunnel. A lab report is written reporting the findings. Level III Students are introduced to the concept of flow separation and backflow. Students are provided a venturi design criteria chart. Venturi B geometry is provided to the students for them to measure. (Venturi B is poorly designed by intent) Students are asked to predict the performance of Venturi B. Students compare their predictions to actual pressure and velocities measured in the wind tunnel. A lab report is written reporting the findings.
27 LESSON PLAN I VENTURI INSERT Level I Title: Law of Continuity Introduction: The continuity equation can be used to explain why the flow of a fluid (or air) will change velocity due to the shape of an object. Lesson: 2) In aeronautics the shape of an airfoil will create lift. This is accomplished by increasing the velocity of air over the airfoil. 3) This velocity change because of the shape is due to the Law of Continuity. This law states Density x Area x Velocity = Constant 4) At velocities less than the speed of sound (subsonic) density will not vary. Density can be deleted and the formula can be simplified to AREA x VELOCITY = CONSTANT 5) As fluid flows through a tube and the area (cross section) of the tube changes the velocity of the fluid will change in relation to the area. 6) At low speeds air will have the same properties as a fluid therefore water or fluids can be used to demonstrate these principles. Examples: 2) Water flowing in a river. Ask your students what they think will happen to the speed (velocity) of water flowing in a river as the river banks get narrower. (Area of the river is decreased) 3) Water flowing over a rock 4) Air flowing threw an hour glass shaped object (Venturi) 5) Ask students to think of other examples of objects that effect the speed of air or water
28 TITLE: Continuity Math Worksheet LESSON PLAN I VENTURI INSERT Level I Introduction: The following problems are designed to use with the wind tunnel to verify the answers. The data was collected using a venturi in the test section. Problems: Use the formula V 1 x A 1 = V 2 x A 2 to solve for the following: Change the formula to: V1 = 50 mph A1 = 23.4 A 2 = 29.4 V 2 = V 1 x A 1 A 2
29 LESSON PLAN I VENTURI INSERT Level I Area Rule Practice: All answers should be in standard units. (1) Compute the Velocity (V2) at location 2 for the following problems: (a) A1 = 5 ft 2 V1 = 50 ft / sec A2 = 10 ft 2 (b) A1 = 20 ft 2 V1 = 5 ft / sec A2 = 10 ft 2 (d) A1 = 2 ft 2 V1 = 4 miles / hr A2 = 1 ft 2
30 LESSON PLAN I VENTURI INSERT Level I (2) A 12 inch diameter pipe carries water at a velocity of 15 ft / sec. The pipe must be reduced to 4 inch diameter to fit through a wall. What will the velocity of the water be in the section that fits trough the wall? 4 inch diameter pipe through wall 12 inch diameter pipe 4) Brainstorming Activity: Have students think of other places where they have seen the shape of an object change the speed of air or water. Write there applications below:
31 Laboratory Experiment: Title: Venturi Insert Activities Objective: To obtain a reading from the wind tunnel test section venturi A and use this readings to calculate the velocity at a second point. Safety: Before Operating the Wind Tunnel perform operational run sheet instructions. Tools and equipment: Venturi (A) test section Inserts, 2 Dwyer water manometers, 10 tube water manometer and tygon tubing. Procedure: 3) Remove second countersunk screws and nuts from the front of the test section ( both sides top and bottom) 4) Connect correct tygon numbered tubes to the lower venturi (numbers go at the opposite end from venturi). 17) Install the upper venturi A section centered in the top of the test section using long wood screws (place washer under screws). 18) Feed the 10 tygon tubes from the lower section through the hole in the center of the test section. As the venturi is brought into place continue pulling tubes (be careful not to disconnect tubes). 19) Once the venturi is centered in the lower test section Install the short wood screws to secure venturi. 20) To aid the airflow tape the leading edge of the venturi sections to the tunnel floor. 21) Connect the numbered tubes to the 10 tube water manometer. 22) Run the wind tunnel and confirm the level of the water in the tubes agrees with the shape of the venturi. If not check for leaks. 23) Using tee fitting connect Dwyer water manometer to the #3 and #8 static ports. 24) Run the wind tunnel and adjust velocity reading from #3 to 45 MPH.
32 25) Measure the distance from the two venturi sections at #3 and #8 static ports. Lines are on the upper test section opposite of the lower ports. 26) Calculate the Area at #3 and #8 ports: Remember Area = Length x Width Test section width = 6.0 if the distance at #3 = 3.9 Area = 6.0 X ) Complete Continuity Math formula to solve for velocity at #8 probe. 28) Run the wind tunnel and check agreement of your answer. (Your answer should agree within 5% of calculated reading.) 29) Repeat the experiment using different velocities. 30) Complete the Continuity Table Area calculation table: Static port # Tunnel Width Distance Between Ports AREA
33 LESSON PLAN VENTURI INSERT Level I Prepare a run sheet that converts the desired set point velocity in miles/hr to feet/second to be read on probe #1. Also include columns for theoretical values of the velocity reading at probe #2 in feet per second and in miles per hour. Compare these to the actual velocities measured by running this experiment under the supervision of your instructor. Write in the actual velocity readings in your run log. Write a lab report discussing your procedure and results. EXPERIMENT #1 Proof of Area Rule Date of Experiment: Purpose: Team Members:
34 LESSON PLAN VENTURI INSERT Level II Teacher s Notes Title: Air Velocity Measurement Calculation Introduction: Velocity ( speed of the air ) is obtained from reading the air pressure. Lesson: 2) To perform aeronautical calculations we must be able to measure the velocity of the air. One of the more accurate means to accomplish this is to use Bernoulli s equation: As the velocity increases  pressure decreases 3) By using a pressure reading in Inches of Water (pressure) we are able to calculate the velocity of the air. 4) Several steps must be taken to modify Bernoulli s equation for the purpose we need. P T = P S 1 + ρ v 2 2 VELOCITY must be moved to the left side of the equation P T P ρ v 2 S = To solve for P Subtract the Wind Tunnel Total pressure From the static pressure reading 1 2 P = 1 2 ρ v 2 2 P = ρ v 2 To simplify ROH ρ Multiply P x 2
35 To move ROH to the left side of the equation 2 ρ P = v 2 To solve for velocity squared take the square root of the left side 2 ρ P = v We are now able to solve for velocity by taking the square root of P x 2 divided by Given the following static pressure readings solve for velocity remember the pressure readings are in inches of water and must first be converted to PSF (Inches of water x x 144) NOTE: For our purposes tunnel pressure is considered to be 0 To convert feet per second to miles per hour (mph) multiply by SAMPLE PROBLEM: 1) Convert (4.07) in. H20 to Velocity Step 1) P = (4.07)  0 = 4.07 in. H20 Step 2) 4.07 x = PSI x 144 = PSF Step 3) 2 x P = Step 4) / = 17, Step 5) sq root of 17, = feet per second(fps) Step 6) x.6818 = mph Answer: 91 mph
36 BERNOULLI FORMULA PRACTICE All answers should be in standard units. VENTURI INSERT Level II (1) Compute the pressure related to a velocity of: (a) 100 ft/sec 2 (b) 100 miles/hr (2) What velocity exists if the following pressure is measured? (a) 75 lb/ft 2 (b) 0.25 lb/in 2 (c) 5 in H 2 0 (3) At the entrance to a tunnel test section the area is 2 ft 2. The pressure is measured to be 1 in H 2 0. Compute the pressure at the exit of the test section where the area is 2 ft 2.
37 Laboratory Experiment Level II Title: Air Velocity Calculation Objective: The student will be able to calculate the air velocity in the wind tunnel using the Bernoulli formula. Set up a spreadsheet to enter the data and formula for velocity Safety: Before operating the wind tunnel perform operational run sheet Tools and Equipment: Venturi A test section insert, 2 Dwyer water manometers, 10 tube water manometer and tygon tubing Procedure: 3) Remove second countersunk screws and nuts from the front of the test section ( both sides top and bottom) 4) Connect correct tygon numbered tubes to the lower venturi (numbers go at the opposite end from venturi). 14) Install the upper venturi A section centered in the top of the test section using long wood screws (place washer under screws). 15) Feed the 10 tygon tubes from the lower section through the hole in the center of the test section. As the venturi is brought into place continue pulling tubes (be careful not to disconnect tubes). 16) Once the venturi is centered in the lower test section Install the short wood screws to secure venturi. 17) To aid the airflow tape the leading edge of the venturi sections to the tunnel floor. 18) Connect the numbered tubes to the 10 tube water manometer. 19) Run the wind tunnel and confirm the level of the water in the tubes agrees with the shape of the venturi. If not check for leaks. 20) Using tee fitting connect Dwyer water manometer to the #3 and #8 static ports. 21) Run the wind tunnel and adjust velocity reading from #3 to 1 Water 22) Calculate the velocity in MPH and FPS solve for velocity at probe #8 and determine the correct reading in Inches of Water. 23) Repeat this experiment at several tunnel velocities (at least 3). Create a
38 spreadsheet in column format that computes the predicted pressures and velocities from the area you measured. The second section of the spreadsheet should calculate the velocity from the measured pressure. Make a column that computes the difference between the measured and predicted velocity. This is the absolute error. In the final column, divide the absolute error by the predicted velocity. This is called the relative error. Your relative error should be less than +/ 5%. 24) Write a lab report discussing your procedure and results. You should discuss the accuracy of your results. In particular, discuss the difference between predicted, calculated, and measured values. Which is the correct result? Date of Experiment: Purpose: Team Members: DESIRED TUNNEL VELOCITY: ACTUAL TUNNEL VELOCITY: TAP # AREA PREDICTED VELOCITY PREDICTED PRESSURE MEASURED PRESSURE CALCULATED VELOCITY Observations:
39 LESSON PLAN I VENTURI INSERT Level III Teacher s Notes: The 3rd level incorporates advanced critical thinking and analysis. Students will be given engineering diagram charts to interpret. These charts are not based on exact formulas. A second venturi insert is provided which violates the design charts. Students should be able to use the charts to predict the poor performance. They should be recognize the scientific principle that explains the difference between data obtained and the calculated data. A venturi has a design limitation based on the geometric angle of divergence. The area of the tunnel or venturi decreases from the entrance to the throat of the venturi. The throat of the venturi is the minimum area. After that point, the flow area will increase. As an exercise in Level III you will have the students plot the pressure using knowledge from Levels I & II (area rule and Bernoulli s equation) versus distance in the venturi from entrance to exit. They should note that will from the entrance to the throat the pressure decrease as the area decreases. Then after the throat the area increases so the pressure will decrease. Ask the students if they think there will be any difference in the flow quality before and after the throat. (There will be.) Air flow naturally wants to move from high pressure to low pressure (give an example of letting air out of a balloon). The students should see that the pressure in the venturi does move from high pressure to low pressure in the entrance. But after the throat the flow is going from low to high pressure. This is unnatural and will only occur when air is forced. Students should recognize that it is possible something different should happen. Refer to figure 1. In the inlet, since the air is being compressed (low to high pressure) it can easily follow converging (or decreasing area) wall angles. It can do so up to 45. Show the venturi or venturi drawing to the students to illustrate this. However, since the flow does not move from the low pressure to high pressure as well, it can not follow the wall diverging (increasing area) angle. If this angle is too great, the flow will separate. (this provides an insight to stall in the next lesson plan) This means that there is an area near the wall where the velocity is near zero. In extreme cases, flow in the opposite direction may occur (backflow). In practice what this means is the equations are no longer accurate if you exceed a divergence angle of 10. Venturi B does have a divergence angle of greater than 10 and the data will not agree with predictions. The error increases with velocity and area. This concept of a difference between assumptions and measurements is referred to in the Proficiency Test. The Venturi Design Chart provides the design criteria.
40
41 PRESSURE PROFILE WORKSHEET LESSON PLAN I VENTURI INSERT Level III Using the chart provided compute the pressure through the venturi form the inlet through the throat and from the throat to the exit. The locations of the pressure taps are provided. The pressure at these locations should be plotted plus a point halfway in between each tap. Do this for each venturi on the graph provided. Discuss with the class and your teacher your results. Is there a difference in the pressure before and after the venturi throat? The chart provided is a venturi design chart. If a venturi is well designed it should perform well. Good performance is defined if the actual pressure and velocity readings agree with the calculated values. If a venturi is poorly designed the measured values will not agree with the calculated. The chart requires that you measure the certain dimensions on the venturi. Do this on the worksheet provided. VENTURI Length, L Width, W Angle, Θ 2 x Θ Stall? A B According to the venturi design chart which venturi is a better design?
42 LESSON PLAN I AIRFOIL SECTION Level I AIRFOIL TERMINOLOGY The following terms will be used in this lesson plan: Leading Edge  The front of the airfoil (tip). Trailing Edge  The aft (rear) edge of the airfoil. Chord or Chordline  An imaginary straight line which passes through an airfoil or wing section from the leading to trailing edge. Chord Length  Distance between the leading and trailing edges of an airfoil. Angle of Attack  The angle formed between the wind striking an airfoil and the chordline of the airfoil. Camberline (meanline)  a line connecting all points midway between the upper and lower surfaces of the airfoil. Camber  A perpendicular distance between the shoreline and the camberline. Symmetrical Airfoil  A airfoil that has the same shape on both sides of its centerline. Asymmetrical Airfoil  A airfoil that has a different upper shape than lower shape. (cambered airfoil). Wing Span  The length of an aircraft wing (when the aircraft is viewed headon). Delta  Difference between static and dynamic pressure ( Ρ). Roh ρ  air density at standard day ( slugs per cubic foot). Alpha α  angle of attack in degrees. Coefficient  A dimensionless number used to express magnitude.
43 LESSON PLAN I AIRFOIL SECTION Level I AIRFOIL GEOMETRY
44 LESSON PLAN I AIRFOIL SECTION Level I SCALING LAW Geometric Similarity is the engineering term used to describe the rules that allow a scale model of an aerodynamic object to be tested. Usually, due to limited space, an object is scaled down. An example is a 1/32nd scale hobbymodel aircraft. Engineers use scale models to test various designs and learn about basic theory. Each dimension of the object should be scaled in order to be geometrically similar. In the above example, the length, height, and width would be multiplied by 1/32. An F16 aircraft that has a wing span of 31 ft., a length of 47 ft., 8 in., and a height of 16 ft. 5 in. The wing area is square feet. At this scale, the model would have a wing span of 11 5 / 8 in., a length of 1 ft., 5 7 / 8 in., and a height of 6 1 / 8 in. The wing area would be 4 5 / 8 square inches. Note that since area has two dimensions, the full scale number was divided by (1/32) squared. In order to isolate the primary force, sometimes only one dimension is scaled. An example is the difference between scaling a wing (area) and an airfoil (length). Since the airfoil shape is usually constant at any point along the span of the wing, the airflow characteristics or pressure over the wing section will be the same all along the wing span. The primary force due to the pressure doesn t change along the wing span. However, as will be seen in the experiments, the pressure changes dramatically along the chord. This is why the wing is scaled in only one direction  the chord. This deliberate scaling in only one direction is called the characteristic dimension. There are some differences due end effects. End effects are from the fuselage and the wing tip can also be tested. This generally has small effects on lift. The airfoil characteristic dimension is the chord length, c (see figure). The ratio between the chord length of the tunnel model airfoil and the prototype airfoil is the scale of the model. The chord lengths must be in the same units so that the scale will be dimensionless. When the geometric similarity occurs, the primary forces on the object will also be scaled. For the airfoil example, the primary force is lift. Therefore if a 1/10th scale airfoil is tested in a wind tunnel, the lift measured will be 1/10th of the lift on the fullscale airfoil. To obtain the lift expected on the fullscale airfoil, multiply by 10. In order to minimize the effect of scaling on the answer, and also to eliminate confusion over whether English or SI units are chosen, aerodynamic forces are expressed in dimensionless coefficient form. The actual physical parameter (force or pressure) is divided by a combination of geometric and flow conditions. The specific combination of parameters has generally been identified in advance from historical research.
45 If the nondimensionalizing parameter has been properly chosen, it will cause data taken at many different conditions to collapse to a single line, thus eliminating the need to take data at each and every condition. (Incidentally, identification of nondimensional parameters by a researcher is a worthy achievement. It usually signifies an new understanding of a phenomenon and leads to engineering development). The first dimensionless coefficients used in this lesson plan is the pressure coefficient. The pressure coefficient (sometimes called the coefficient of pressure) is defined as: C p = P s P ( ρ / g o ) V Where the following symbols are defined as: C p = Pressure Coefficient (dimensionless). P s = Pressure in physical units on airfoil surface ( lb / ft 2 ). P = Pressure in physical units at infinity ( lb / ft 2 ). r = Density ( lb / ft 3 ). g 0 = Gravitational constant (32.2 ft / sec 2 ). V 0 = Tunnel Velocity ( ft / sec ). As you can see the units cancel: [( lb / ft 2 )( ft / sec 2 )]/[( lb / ft 3 )( ft / sec ) 2 ]. The quantity in the denominator is called the dynamic pressure, q. It has units of pressure and is the pressure caused by velocity. C p = P s P q This formula can be manipulated when taking data in the wind tunnel, using the following physical interpretation (since the reading is often referenced to the atmospheric pressure): P s = P reading + P atm and P = P tunnel static P s  P = P reading + P atm  P tunnel static If there are no losses in the tunnel, the total pressure is equal to the atmospheric pressure. P s  P = P reading + P total  P tunnel static
46 The dynamic pressure was defined earlier as the difference between the total and static pressures. (See the general and Venturi lesson plans). P total = P tunnel static + P dynamic P total = P tunnel static + q rearranging; P total  P tunnel static = q P s  P = P reading + ( P total  P tunnel static ) = P reading + q So finally, the wind tunnel format for pressure coefficient is: C p = P + rdg q q P rdg = q + 1
Lift and Drag on an Airfoil ME 123: Mechanical Engineering Laboratory II: Fluids
Lift and Drag on an Airfoil ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction In this lab the characteristics of airfoil lift, drag,
More informationNACA Nomenclature NACA 2421. NACA Airfoils. Definitions: Airfoil Geometry
0.40 m 0.21 m 0.02 m NACA Airfoils 6Feb08 AE 315 Lesson 10: Airfoil nomenclature and properties 1 Definitions: Airfoil Geometry z Mean camber line Chord line x Chord x=0 x=c Leading edge Trailing edge
More informationHead Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids
Head Loss in Pipe Flow ME 123: Mechanical Engineering Laboratory II: Fluids Dr. J. M. Meyers Dr. D. G. Fletcher Dr. Y. Dubief 1. Introduction Last lab you investigated flow loss in a pipe due to the roughness
More informationFLUID FLOW Introduction General Description
FLUID FLOW Introduction Fluid flow is an important part of many processes, including transporting materials from one point to another, mixing of materials, and chemical reactions. In this experiment, you
More informationThe aerodynamic center
The aerodynamic center In this chapter, we re going to focus on the aerodynamic center, and its effect on the moment coefficient C m. 1 Force and moment coefficients 1.1 Aerodynamic forces Let s investigate
More informationAOE 3134 Complete Aircraft Equations
AOE 3134 Complete Aircraft Equations The requirements for balance and stability that we found for the flying wing carry over directly to a complete aircraft. In particular we require the zerolift pitch
More informationExperiment 3 Pipe Friction
EML 316L Experiment 3 Pipe Friction Laboratory Manual Mechanical and Materials Engineering Department College of Engineering FLORIDA INTERNATIONAL UNIVERSITY Nomenclature Symbol Description Unit A crosssectional
More informationApplied Fluid Mechanics
Applied Fluid Mechanics 1. The Nature of Fluid and the Study of Fluid Mechanics 2. Viscosity of Fluid 3. Pressure Measurement 4. Forces Due to Static Fluid 5. Buoyancy and Stability 6. Flow of Fluid and
More informationPacific Pump and Power
Pacific Pump and Power 91503 Nukuawa Street Kapolei, Hawaii 96707 Phone: (808) 6728198 or (800) 9755112 Fax: (866) 4240953 Email: sales@pacificpumpandpower.com Web: www.pacificpumpandpower.com Table
More informationPropeller Efficiency. Rule of Thumb. David F. Rogers, PhD, ATP
Propeller Efficiency Rule of Thumb David F. Rogers, PhD, ATP Theoretically the most efficient propeller is a large diameter, slowly turning single blade propeller. Here, think the Osprey or helicopters.
More informationHow do you compare numbers? On a number line, larger numbers are to the right and smaller numbers are to the left.
The verbal answers to all of the following questions should be memorized before completion of prealgebra. Answers that are not memorized will hinder your ability to succeed in algebra 1. Number Basics
More informationPS High Wind Speed Forces (2/25/2007)
This report is intended to give a familiarity with the forces of wind. It is intended to aid in the building of polar shift survival quarters by giving engineering design considerations. The force of wind
More informationPipe Sizes For Water Distribution System Design
Appendix D Pipe Sizes For Water Distribution System Design D. This appendix contains information to help determine pipe sizes when designing a water distribution system. Use Table D and Tables D through
More informationQuick Reference ebook
This file is distributed FREE OF CHARGE by the publisher Quick Reference Handbooks and the author. Quick Reference ebook Click on Contents or Index in the left panel to locate a topic. The math facts listed
More informationPractice Problems on Boundary Layers. Answer(s): D = 107 N D = 152 N. C. Wassgren, Purdue University Page 1 of 17 Last Updated: 2010 Nov 22
BL_01 A thin flat plate 55 by 110 cm is immersed in a 6 m/s stream of SAE 10 oil at 20 C. Compute the total skin friction drag if the stream is parallel to (a) the long side and (b) the short side. D =
More informationWorking Math Formulas, Units, Conversions
Working Math Formulas, Units, Conversions This presentation has been adapted from Math for Subsurface Operators given at the North Carolina Subsurface Operator School Math will be used to Determine a flow
More informationis the stagnation (or total) pressure, constant along a streamline.
70 Incompressible flow (page 60): Bernoulli s equation (steady, inviscid, incompressible): p 0 is the stagnation (or total) pressure, constant along a streamline. Pressure tapping in a wall parallel to
More informationApplication of CFD Simulation in the Design of a Parabolic Winglet on NACA 2412
, July 24, 2014, London, U.K. Application of CFD Simulation in the Design of a Parabolic Winglet on NACA 2412 Arvind Prabhakar, Ayush Ohri Abstract Winglets are angled extensions or vertical projections
More informationWindow Glass Design 5 According to ASTM E 1300
A User s Guide to: Window Glass Design 5 According to ASTM E 1300 A product of: 1 Table of Contents Table of Contents List of Figures Chapter 1: Window Glass Design 5 1.1 Introduction 1.2 Features ii iv
More informationAlgebra I. In this technological age, mathematics is more important than ever. When students
In this technological age, mathematics is more important than ever. When students leave school, they are more and more likely to use mathematics in their work and everyday lives operating computer equipment,
More informationSIMPLIFIED METHOD FOR ESTIMATING THE FLIGHT PERFORMANCE OF A HOBBY ROCKET
SIMPLIFIED METHOD FOR ESTIMATING THE FLIGHT PERFORMANCE OF A HOBBY ROCKET WWW.NAKKAROCKETRY.NET February 007 Rev.1 March 007 1 Introduction As part of the design process for a hobby rocket, it is very
More informationGeometry Solve real life and mathematical problems involving angle measure, area, surface area and volume.
Performance Assessment Task Pizza Crusts Grade 7 This task challenges a student to calculate area and perimeters of squares and rectangles and find circumference and area of a circle. Students must find
More informationEVALUATION OF EXHAUST VENTILATION SYSTEMS
HSCI 348 Industrical Hygiene Instrumentation Techniques Laboratory No. 5 EVALUATION OF EXHAUST VENTILATION SYSTEMS INTRODUCTION: Of major concern to the Industrial Hygienist is the evaluation and control
More informationN Q.3 Choose a level of accuracy appropriate to limitations on measurement when reporting quantities.
Performance Assessment Task Swimming Pool Grade 9 The task challenges a student to demonstrate understanding of the concept of quantities. A student must understand the attributes of trapezoids, how to
More informationAcceleration of Gravity Lab Basic Version
Acceleration of Gravity Lab Basic Version In this lab you will explore the motion of falling objects. As an object begins to fall, it moves faster and faster (its velocity increases) due to the acceleration
More informationMEASUREMENT. Historical records indicate that the first units of length were based on people s hands, feet and arms. The measurements were:
MEASUREMENT Introduction: People created systems of measurement to address practical problems such as finding the distance between two places, finding the length, width or height of a building, finding
More informationAOE 3104 Aircraft Performance Problem Sheet 2 (ans) Find the Pressure ratio in a constant temperature atmosphere:
AOE 3104 Aircraft Performance Problem Sheet 2 (ans) 6. The atmosphere of Jupiter is essentially made up of hydrogen, H 2. For Hydrogen, the specific gas constant is 4157 Joules/(kg)(K). The acceleration
More informationPrinciples of glider flight
Principles of glider flight [ Lift, drag & glide performance ] Richard Lancaster R.Lancaster@carrotworks.com ASK21 illustrations Copyright 1983 Alexander Schleicher GmbH & Co. All other content Copyright
More informationFractions, Ratios, and Proportions Work Sheets. Contents
Fractions, Ratios, and Proportions Work Sheets The work sheets are grouped according to math skill. Each skill is then arranged in a sequence of work sheets that build from simple to complex. Choose the
More informationForces on a Model Rocket
Forces on a Model Rocket This pamphlet was developed using information for the Glenn Learning Technologies Project. For more information, visit their web site at: http://www.grc.nasa.gov/www/k12/aboutltp/educationaltechnologyapplications.html
More informationMcDougal Littell California:
McDougal Littell California: PreAlgebra Algebra 1 correlated to the California Math Content s Grades 7 8 McDougal Littell California PreAlgebra Components: Pupil Edition (PE), Teacher s Edition (TE),
More informationCivil Engineering Hydraulics Mechanics of Fluids. Flow in Pipes
Civil Engineering Hydraulics Mechanics of Fluids Flow in Pipes 2 Now we will move from the purely theoretical discussion of nondimensional parameters to a topic with a bit more that you can see and feel
More informationExhaust Calculation Booklet
Exhaust Calculation Booklet American Dryer Corporation 88 Currant Road Fall River MA 027204781 Telephone: (508) 6789000 / Fax: (508) 6789447 email: techsupport@amdry.com ADC Part No. 450450 Exhaust
More informationOpen Channel Flow Measurement Weirs and Flumes
Open Channel Flow Measurement Weirs and Flumes by Harlan H. Bengtson, PhD, P.E. 1. Introduction Your Course Title Here Measuring the flow rate of water in an open channel typically involves some type of
More informationSIZING AND CAPACITIES OF GAS PIPING
APPENDIX A (IFGS) SIZING AND CAPACITIES OF GAS PIPING (This appendix is informative and is not part of the code.) A.1 General. To determine the size of piping used in a gas piping system, the following
More informationWHAT IS AREA? CFE 3319V
WHAT IS AREA? CFE 3319V OPEN CAPTIONED ALLIED VIDEO CORPORATION 1992 Grade Levels: 59 17 minutes DESCRIPTION What is area? Lesson One defines and clarifies what area means and also teaches the concept
More informationPOLYNOMIAL FUNCTIONS
POLYNOMIAL FUNCTIONS Polynomial Division.. 314 The Rational Zero Test.....317 Descarte s Rule of Signs... 319 The Remainder Theorem.....31 Finding all Zeros of a Polynomial Function.......33 Writing a
More informationVACUUM TESTING PRECAST CONCRETE MANHOLES
1 OF 5 testing is a quick, safe and practical way to validate manhole system integrity. Manhole sections can be tested at the precast concrete plant prior to delivery or on site prior to backfilling. Here
More informationCHAPTER 2 HYDRAULICS OF SEWERS
CHAPTER 2 HYDRAULICS OF SEWERS SANITARY SEWERS The hydraulic design procedure for sewers requires: 1. Determination of Sewer System Type 2. Determination of Design Flow 3. Selection of Pipe Size 4. Determination
More informationBasic Math for the Small Public Water Systems Operator
Basic Math for the Small Public Water Systems Operator Small Public Water Systems Technology Assistance Center Penn State Harrisburg Introduction Area In this module we will learn how to calculate the
More informationMeasurement with Ratios
Grade 6 Mathematics, Quarter 2, Unit 2.1 Measurement with Ratios Overview Number of instructional days: 15 (1 day = 45 minutes) Content to be learned Use ratio reasoning to solve realworld and mathematical
More information5.1Angles and Their Measure
5.1Angles and Their Measure Objectives: 1. Find the degree or radian measure of coterminal angles. 2. Convert between degrees minutes and seconds and decimal degrees. 3. Convert between degrees and radians.
More informationMATH 110 Landscape Horticulture Worksheet #4
MATH 110 Landscape Horticulture Worksheet #4 Ratios The math name for a fraction is ratio. It is just a comparison of one quantity with another quantity that is similar. As a Landscape Horticulturist,
More informationG C.3 Construct the inscribed and circumscribed circles of a triangle, and prove properties of angles for a quadrilateral inscribed in a circle.
Performance Assessment Task Circle and Squares Grade 10 This task challenges a student to analyze characteristics of 2 dimensional shapes to develop mathematical arguments about geometric relationships.
More information1 foot (ft) = 12 inches (in) 1 yard (yd) = 3 feet (ft) 1 mile (mi) = 5280 feet (ft) Replace 1 with 1 ft/12 in. 1ft
2 MODULE 6. GEOMETRY AND UNIT CONVERSION 6a Applications The most common units of length in the American system are inch, foot, yard, and mile. Converting from one unit of length to another is a requisite
More informationEXPONENTS. To the applicant: KEY WORDS AND CONVERTING WORDS TO EQUATIONS
To the applicant: The following information will help you review math that is included in the Paraprofessional written examination for the Conejo Valley Unified School District. The Education Code requires
More informationElectric Motors and Drives
EML 2322L MAE Design and Manufacturing Laboratory Electric Motors and Drives To calculate the peak power and torque produced by an electric motor, you will need to know the following: Motor supply voltage,
More informationR = 1545 ftlbs/lb mole ºR R = 1.986 BTU/lb mole ºR R = 1.986 cal/gm mole ºK
Flow Through the Regulator The SCUBA tank regulator arrangement can be idealized with the diagram shown below. This idealization is useful for computing pressures and gas flow rates through the system.
More informationCharlesworth School Year Group Maths Targets
Charlesworth School Year Group Maths Targets Year One Maths Target Sheet Key Statement KS1 Maths Targets (Expected) These skills must be secure to move beyond expected. I can compare, describe and solve
More informationLab 1a Wind Tunnel Testing Principles & Lift and Drag Coefficients on an Airfoil
Lab 1a Wind Tunnel Testing Principles & Lift and Drag Coefficients on an Airfoil OBJECTIVES  Calibrate the RPM/wind speed relation of the wind tunnel.  Measure the drag and lift coefficients of an airfoil
More informationWind Load Analysis. Silent Sentinel Arrow Board. Silent Messenger Message Board. Silent Messenger II Message Board
Wind Load Analysis Silent Sentinel Arrow Board Silent Messenger Message Board Silent Messenger II Message Board Silent Messenger II Lift & Rotate Message Board WIND STABILITY ANALYSIS SOLAR TECHNOLOGY
More informationNACA airfoil geometrical construction
The NACA airfoil series The early NACA airfoil series, the 4digit, 5digit, and modified 4/5digit, were generated using analytical equations that describe the camber (curvature) of the meanline (geometric
More informationA Guide to Calculate Convection Coefficients for Thermal Problems Application Note
A Guide to Calculate Convection Coefficients for Thermal Problems Application Note Keywords: Thermal analysis, convection coefficients, computational fluid dynamics, free convection, forced convection.
More informationMathUSee Correlation with the Common Core State Standards for Mathematical Content for Fourth Grade
MathUSee Correlation with the Common Core State Standards for Mathematical Content for Fourth Grade The fourthgrade standards highlight all four operations, explore fractions in greater detail, and
More informationCalculating Area, Perimeter and Volume
Calculating Area, Perimeter and Volume You will be given a formula table to complete your math assessment; however, we strongly recommend that you memorize the following formulae which will be used regularly
More informationSolving Geometric Applications
1.8 Solving Geometric Applications 1.8 OBJECTIVES 1. Find a perimeter 2. Solve applications that involve perimeter 3. Find the area of a rectangular figure 4. Apply area formulas 5. Apply volume formulas
More informationAP Physics 1 Summer Assignment
AP Physics 1 Summer Assignment AP Physics 1 Summer Assignment Welcome to AP Physics 1. This course and the AP exam will be challenging. AP classes are taught as college courses not just collegelevel courses,
More informationAerodynamic Design Optimization Discussion Group Case 4: Single and multipoint optimization problems based on the CRM wing
Aerodynamic Design Optimization Discussion Group Case 4: Single and multipoint optimization problems based on the CRM wing Lana Osusky, Howard Buckley, and David W. Zingg University of Toronto Institute
More informationGeometry and Measurement
The student will be able to: Geometry and Measurement 1. Demonstrate an understanding of the principles of geometry and measurement and operations using measurements Use the US system of measurement for
More informationOne basic concept in math is that if we multiply a number by 1, the result is equal to the original number. For example,
MA 35 Lecture  Introduction to Unit Conversions Tuesday, March 24, 205. Objectives: Introduce the concept of doing algebra on units. One basic concept in math is that if we multiply a number by, the result
More informationThis assignment will help you to prepare for Algebra 1 by reviewing some of the things you learned in Middle School. If you cannot remember how to complete a specific problem, there is an example at the
More informationThe entire document shall be read and understood before proceeding with a test. ISTA 3B 2013  Page 1 of 35
PackagedProducts for LessThanTruckload (LTL) Shipment ISTA 3 Series General Simulation Performance Test PROCEDURE VERSION DATE Last TECHNICAL Change: NOVEMBER 2012 Last EDITORIAL Change: JANUARY 2013
More informationThin Airfoil Theory. Charles R. O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 74078
13 Thin Airfoil Theory Charles R. O Neill School of Mechanical and Aerospace Engineering Oklahoma State University Stillwater, OK 7478 Project One in MAE 3253 Applied Aerodynamics and Performance March
More informationThe Versatile Differential Pressure Transmitter. By David Gunn Honeywell Process Solutions
The Versatile Differential Pressure Transmitter By David Gunn Honeywell Process Solutions The Versatile Differential Pressure Transmitter 2 Table of Contents Abstract... 3 Pressure Fundamentals... 3 Applications...
More informationSTUDENT MANUAL HEAVY EQUIPMENT & RIGGING SPECIALIST TRAINING MODULE 2 UNIT 2: CALCULATING WEIGHTS & CENTER OF GRAVITY
STUDENT MANUAL HEAVY EQUIPMENT & RIGGING SPECIALIST TRAINING MODULE 2 UNIT 2: CALCULATING WEIGHTS & CENTER OF GRAVITY Unit Objective Enabling Objectives Upon completion of this unit, you will be able to
More informationAE 430  Stability and Control of Aerospace Vehicles
AE 430  Stability and Control of Aerospace Vehicles Atmospheric Flight Mechanics 1 Atmospheric Flight Mechanics Performance Performance characteristics (range, endurance, rate of climb, takeoff and landing
More informationThe University of Toledo Soil Mechanics Laboratory
The University of Toledo Soil Mechanics Laboratory Permeability Testing  1 Constant and Falling Head Tests Introduction In 1856 the French engineer Henri D arcy demonstrated by experiment that it is possible
More informationPerimeter, Area, and Volume
Perimeter is a measurement of length. It is the distance around something. We use perimeter when building a fence around a yard or any place that needs to be enclosed. In that case, we would measure the
More informationAlgebra 1 2008. Academic Content Standards Grade Eight and Grade Nine Ohio. Grade Eight. Number, Number Sense and Operations Standard
Academic Content Standards Grade Eight and Grade Nine Ohio Algebra 1 2008 Grade Eight STANDARDS Number, Number Sense and Operations Standard Number and Number Systems 1. Use scientific notation to express
More information1. Which of the 12 parent functions we know from chapter 1 are power functions? List their equations and names.
Pre Calculus Worksheet. 1. Which of the 1 parent functions we know from chapter 1 are power functions? List their equations and names.. Analyze each power function using the terminology from lesson 1.
More informationTyphoon Haiyan 1. Force of wind blowing against vertical structure. 2. Destructive Pressure exerted on Buildings
Typhoon Haiyan 1. Force of wind blowing against vertical structure 2. Destructive Pressure exerted on Buildings 3. Atmospheric Pressure variation driving the Typhoon s winds 4. Energy of Typhoon 5. Height
More informationAN EXPLANATION OF JOINT DIAGRAMS
AN EXPLANATION OF JOINT DIAGRAMS When bolted joints are subjected to external tensile loads, what forces and elastic deformation really exist? The majority of engineers in both the fastener manufacturing
More informationPolynomial Degree and Finite Differences
CONDENSED LESSON 7.1 Polynomial Degree and Finite Differences In this lesson you will learn the terminology associated with polynomials use the finite differences method to determine the degree of a polynomial
More informationREVIEW SHEETS INTRODUCTORY PHYSICAL SCIENCE MATH 52
REVIEW SHEETS INTRODUCTORY PHYSICAL SCIENCE MATH 52 A Summary of Concepts Needed to be Successful in Mathematics The following sheets list the key concepts which are taught in the specified math course.
More information2 1/2 Pipe. 40 = height. the gauge pressure inside the vessel from the gauge pressure at the nozzle inlet as shown:
116eering. Engineering. Engineering. Engineering. Engineerin Engineering Information SPECIFYING SPRAY NOZZLES Spray nozzles have three basic functions: meter flow distribute liquid break up a liquid stream
More informationWing Design: Major Decisions. Wing Area / Wing Loading Span / Aspect Ratio Planform Shape Airfoils Flaps and Other High Lift Devices Twist
Wing Design: Major Decisions Wing Area / Wing Loading Span / Aspect Ratio Planform Shape Airfoils Flaps and Other High Lift Devices Twist Wing Design Parameters First Level Span Area Thickness Detail Design
More informationLecture 5 : Solving Equations, Completing the Square, Quadratic Formula
Lecture 5 : Solving Equations, Completing the Square, Quadratic Formula An equation is a mathematical statement that two mathematical expressions are equal For example the statement 1 + 2 = 3 is read as
More informationWhat are the place values to the left of the decimal point and their associated powers of ten?
The verbal answers to all of the following questions should be memorized before completion of algebra. Answers that are not memorized will hinder your ability to succeed in geometry and algebra. (Everything
More informationMichael Montgomery Marketing Product Manager Rosemount Inc. Russ Evans Manager of Engineering and Design Rosemount Inc.
ASGMT / Averaging Pitot Tube Flow Measurement Michael Montgomery Marketing Product Manager Rosemount Inc. Russ Evans Manager of Engineering and Design Rosemount Inc. Averaging Pitot Tube Meters Introduction
More informationUnit 4 Multiplication of Whole Numbers. Work Space
34 Section 1 Whole Numbers Work Space Unit 4 Multiplication of Whole Numbers Key Terms carry multiplicand multiplication multiplier product Introduction Multiplication can be thought of as a fast way to
More informationMacroFlo Opening Types User Guide <Virtual Environment> 6.0
MacroFlo Opening Types User Guide 6.0 Page 1 of 18 Contents 1. Introduction...4 2. What Are Opening Types?...5 3. MacroFlo Opening Types Manager Interface...5 3.1. Add... 5 3.2. Reference
More informationA=b h= 83 in. 45ft. ft. = ft.2
The Easiest Way to Convert Units in an Algebraic Equation Physics professors teach you to convert everything into standard SI units, solve the problem, and hope the units come out right. In Chemistry and
More informationFigure 1. Head losses in a pipe
53:071 Principles of Hydraulics Laboratory Experiment #1 ENERGY AND HYDRAULIC GRADE LINES IN WATER PIPE SYSTEMS Principle The energy of a real fluid decreases as it moves through a pipe. The energy budget
More informationEach table shows the pressure drop for two lengths of pipe, enabling the user to estimate the drop for a shorter or greater length of pipe.
Bulletin 3006ENG Flow Table Cover ENGINEERING Flow Tables Criteria for Selection of the proper components for a fluid flow system: Line Pressure (Usually a fixed quantity) Flow Rate Required Size of Pipe
More informationAnswer Key For The California Mathematics Standards Grade 7
Introduction: Summary of Goals GRADE SEVEN By the end of grade seven, students are adept at manipulating numbers and equations and understand the general principles at work. Students understand and use
More informationThe Base Shear Formula
The Base Shear Formula You will have to do a bit of arithmetic and use a very simple formula known as the base shear formula to determine exactly how many bolts, how much plywood, and how many shear transfer
More informationWhen the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid.
Fluid Statics When the fluid velocity is zero, called the hydrostatic condition, the pressure variation is due only to the weight of the fluid. Consider a small wedge of fluid at rest of size Δx, Δz, Δs
More informationAnalysis of Experimental Uncertainties: Density Measurement Physics Lab II
Analysis of Experimental Uncertainties: Density Measurement Physics Lab II Objective This laboratory exercise allows students to estimate and analyze experimental uncertainties. Students will calculate
More informationPrinciples of Flight. Chapter 3. Introduction. Structure of the Atmosphere
Chapter 3 Principles of Flight Introduction This chapter examines the fundamental physical laws governing the forces acting on an aircraft in flight, and what effect these natural laws and forces have
More informationMathematics as Reasoning Students will use reasoning skills to determine the best method for maximizing area.
Title: A Pen for Penny Brief Overview: This unit is a reinforcement of the concepts of area and perimeter of rectangles. Methods for maximizing area while perimeter remains the same are also included.
More informationDETERMINING TOTAL DYNAMIC HEAD
DETERMINING TOTAL DYNAMIC HEAD The total dynamic head of a water system must be considered when determining the size of pumping equipment to be installed. It determines the various head losses that the
More informationDefinition 8.1 Two inequalities are equivalent if they have the same solution set. Add or Subtract the same value on both sides of the inequality.
8 Inequalities Concepts: Equivalent Inequalities Linear and Nonlinear Inequalities Absolute Value Inequalities (Sections 4.6 and 1.1) 8.1 Equivalent Inequalities Definition 8.1 Two inequalities are equivalent
More informationA. Hyll and V. Horák * Department of Mechanical Engineering, Faculty of Military Technology, University of Defence, Brno, Czech Republic
AiMT Advances in Military Technology Vol. 8, No. 1, June 2013 Aerodynamic Characteristics of MultiElement Iced Airfoil CFD Simulation A. Hyll and V. Horák * Department of Mechanical Engineering, Faculty
More informationA Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion
A Determination of g, the Acceleration Due to Gravity, from Newton's Laws of Motion Objective In the experiment you will determine the cart acceleration, a, and the friction force, f, experimentally for
More informationExperimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION ( )
a. Using Faraday s law: Experimental Question 1: Levitation of Conductors in an Oscillating Magnetic Field SOLUTION The overall sign will not be graded. For the current, we use the extensive hints in the
More informationChapter 3 Process Variables. Mass and Volume
Chapter 3 Process Variables Process: to a chemical engineer, the set of tasks or operations that accomplish a chemical or material transformation to produce a product Feed or inputs: raw materials and
More informationRemoving chips is a method for producing plastic threads of small diameters and high batches, which cause frequent failures of thread punches.
Plastic Threads Technical University of Gabrovo Yordanka Atanasova Threads in plastic products can be produced in three ways: a) by direct moulding with thread punch or die; b) by placing a threaded metal
More informationSince the Steel Joist Institute
SELECTING and SPECIFYING Wesley B. Myers, P.E. An insider s guide to selecting and specifying Kseries, LH, DLHseries joists and joist girders Since the Steel Joist Institute adopted the first standard
More informationModule 9: Basics of Pumps and Hydraulics Instructor Guide
Module 9: Basics of Pumps and Hydraulics Instructor Guide Activities for Unit 1 Basic Hydraulics Activity 1.1: Convert 45 psi to feet of head. 45 psis x 1 ft. = 103.8 ft 0.433 psi Activity 1.2: Determine
More informationChapter 8. Chapter 8 Opener. Section 8.1. Big Ideas Math Green WorkedOut Solutions. Try It Yourself (p. 353) Number of cubes: 7
Chapter 8 Opener Try It Yourself (p. 5). The figure is a square.. The figure is a rectangle.. The figure is a trapezoid. g. Number cubes: 7. a. Sample answer: 4. There are 5 6 0 unit cubes in each layer.
More information